Dataflow analysis Discovering Global Live Ranges of Variables - - PowerPoint PPT Presentation

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Dataflow analysis

Discovering Global Live Ranges

• f Variables

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Optimization and analysis



Requirement for optimizations



Correctness (safety)

 must preserve the meaning of the input computation



Profitability

 must improve code quality



Program analysis



Statically examines input computation to ensure safety and profitability of optimizations



Compile-time reasoning of runtime program behavior

 Undecidable in general due to external program input, complex control flow,

and pointer/array references

 Conservative approximation of program runtime behavior:

may miss opportunities of applying optimization, but ensure all

• ptimizations are correct



Data-flow analysis



Reason about flow of values on control-flow graphs



Example: available expression analysis for global redundancy elimination



Can be used for program optimization or program understanding

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Control-flow graph

 Graphical representation of runtime control-flow paths

 Nodes of graph: basic blocks (straight-line computations)  Edges of graph: flows of control

 Useful for collecting information about computation

 Detect loops, remove redundant computations, register

allocation, instruction scheduling…

 Alternative CFG: Each node contains a single statement

…… i = 0 while (i < 50) { t1 = b * 2; a = a + t1; i = i + 1; } …. if I < 50 …… t1 := b * 2; a := a + t1; i = i + 1; i =0;

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Live variable analysis

 A data-flow analysis problem

 A variable v is live at CFG point p iff there is a path from

p to a use of v along which v is not redefined

 At any CFG point p, what variables are alive?

 Live variable analysis can be used in

 Global register allocation

 Dead variables no longer need to be in registers

 Useless-store elimination

 Dead variable don’t need to be stored back to memory

 Uninitialized variable detection

 No variable should be alive at program entry point

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Computing live variables

 For each basic block n, let

 UEVar(n)=variables used before any definition in n  VarKill(n)=variables defined (modified) in n (killed by n)

S1: m := y * z S2: y := y -z S3: o := y * z M for each basic block n:S1;S2;S3;…;Sk VarKill := ∅ UEVar(n) := ∅ for i = 1 to k suppose Si is “x := y op z” if y ∉ VarKill UEVar(n) = UEVar(n) ∪ {y} if z ∉ VarKill UEVar(n) = UEVar(n) ∪ {z} VarKill = VarKill ∪ {x}

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Computing live variables

 For each basic block n,

let

 UEVar(n)

vars used before defined

 VarKill(n)

vars defined (killed by n)

Goal: evaluate vars alive on exit from n

LiveOut(n)= ∪ m∈succ(n)

(UEVar(m) ∪ (LiveOut(m)-VarKill(m)) m:=a+b n:=a+b p:=c+d r:=c+d q:=a+b r:=c+d e:=b+18 s:=a+b u:=e+f e:=a+17 t:=c+d u:=e+f v:=a+b w:=c+d X:=e+f y:=a+b z:=c+d A B C D E F G

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Algorithm: computing live variables

 For each basic block n, let



UEVar(n)=variables used before any definition in n



VarKill(n)=variables defined (modified) in n (killed by n)

Goal: evaluate names of variables alive on exit from n



LiveOut(n)= ∪ (UEVar(m) ∪ (LiveOut(m) - VarKill(m)) m∈succ(n)

for each basic block bi compute UEVar(bi) and VarKill(bi) LiveOut(bi) := ∅ for (changed := true; changed; ) changed = false for each basic block bi

• ld = LiveOut(bi)

LiveOut(bi)= ∪ (UEVar(m) ∪ (LiveOut(m) - VarKill(m)) if (LiveOut(bi) != old) changed := true m∈succ(bi)

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Iterative dataflow algorithm

 Iterative evaluation of result

sets until a fixed point is reached

 Does the algorithm always

terminate?

 If the result sets are

bounded and grow monotonically, then yes; Otherwise, no.

 Fixed-point solution is

independent of evaluation

• rder

 What answer does the

algorithm compute?

 Unique fixed-point solution  The meet-over-all-paths

solution

 How long does it take the

algorithm to terminate?

 Depends on traversing order

• f basic blocks

for each basic block bi compute Gen(bi) and Kill(bi) Result(bi) := ∅ for (changed := true; changed; ) changed = false for each basic block bi

• ld = Result(bi)

Result(bi)= ∩ or ∪ [m∈pred(bi) or succ(bi)] (Gen(m) ∪ (Result(m)-Kill(m)) if (Result(bi) != old) changed := true

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Traversing order of basic blocks

 Facilitate fast convergence to

the fixed point

 Postorder traversal

 Visits as many of a nodes

successors as possible before visiting the node

 Used in backward data-flow

analysis

 Reverse postorder traversal

 Visits as many of a node’s

predecessors as possible before visiting the node

 Used in forward data-flow

analysis 4 2 3 1 1 3 2 4 postorder Reverse postorder

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More about dataflow analysis

 Sources of imprecision

 Unreachable control flow edges, array and pointer references,

precedure calls

 Other data-flow programs

 Reaching definition analysis

 A definition point d of variable v reaches CFG point p iff there is a

path from d to p along which v is not redefined

 At any CFG point p, what definition points can reach p?

 Very busy expression analysis

 An expression e is very busy at a CFG point p if it is evaluated on

every path leaving p, and evaluating e at p yields the same result.

 At any CFG point p, what expressions are very busy?

 Constant propagation analysis

 A variable-value pair (v,c) is valid at a CFG point p if on every

path from procedure entry to p, variable v has value c

 At any CFG point p, what variables have constants?